计算：1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)

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计算：1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)

计算：1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
计算：1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)

计算：1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
=(1/3)[1/x-1/(x+3)+1/(x+3)-1/(x+6)+---+1/(x+2004)-1/(x+2007)]
=(1/3)[1/x-1/(x+2007)]
=669/(x^2+2007x)

1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
=1/3*[1/x-1/(x+3)]+1/3*[1/(x+3)-1/(x+6)]+……+1/3[1/(x+2004)-1/(x+2007)]
=1/3*[1/x-1/(x+3)+1/(x+3)-1/(x+6)+……+1/(x+2004)-1/(x+2007)]
=1/3*[1/x-1/(x+2007)]
=669/(x^2+2007x)

1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
=1/3[1/X-1/(X+3)]-1/3[1/X+3)-1/(X+6)]+......+1/3[1/(X+2004)
-1/(X+2007)]
=1/3[1/X-1/(X+3)+1/(X+3)-1/(X+6)+1/(X+6)-1/(X+9)+....-1/(X+2004)
+1/(X+2004)-1/(X+2007)]
=1/3[1/X-1/(X+2007)]
=1/3[(X+2007-X)/X(X+2007)]
=1/3[2007/X(X+2007)]
=669/X(X+2007)

1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
=1/3[1/X-1/(X+3)]-1/3[1/X+3)-1/(X+6)]+......+1/3[1/(X+2004)
-1/(X+2007)]
=1/3[1/X-1/(X+3)+1/(X+3)-1/(X+6)+1/(X+6)-1/(X+9)+....-1/(X+2004)

全部展开

1/x(x+3)+1/(x+3)(x+6)+...+1/(x+2004)(x+2007)
=1/3[1/X-1/(X+3)]-1/3[1/X+3)-1/(X+6)]+......+1/3[1/(X+2004)
-1/(X+2007)]
=1/3[1/X-1/(X+3)+1/(X+3)-1/(X+6)+1/(X+6)-1/(X+9)+....-1/(X+2004)
+1/(X+2004)-1/(X+2007)]
=1/3[1/X-1/(X+2007)]
=1/3[(X+2007-X)/X(X+2007)]
=1/3[2007/X(X+2007)]
=669/X(X+2007)
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